Vertical Asymptotes Y-intercepts of Rational Functions Horizontal Asymptotes Domain of Rational...
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Transcript of Vertical Asymptotes Y-intercepts of Rational Functions Horizontal Asymptotes Domain of Rational...
Vertical Asymptote
s
Y-intercept
s of Rational
Functions
Horizontal Asymptot
es
Domain of Rational
Functions
Factoring when a =
1
Factoring when a>1
$ 100 $100 $100 $100 $100 $100$200 $200 $200 $200 $200 $200$300 $300 $300 $300 $300 $300$400 $400 $400 $400 $400 $400
JJΣθPARδYΣθPARδY!! MαthMαth
Mαth JΣθPARδY! was created by GradeAmathmathhelp.com
Rational Rational Functions/Factoring Functions/Factoring
JΣθPARδY!JΣθPARδY!
Vertical Asymptotes - 100
• Determine the location of the vertical asymptote(s) of
x = 2
JJΣθPARδYΣθPARδY!! MαthMαth
Vertical Asymptotes - 200
• Determine the location of the vertical asymptote(s) of
JJΣθPARδYΣθPARδY!! MαthMαth
x = -5
Vertical Asymptotes - 300
• Use the graph to determine the vertical asymptotes
JJΣθPARδYΣθPARδY!! MαthMαth
x = -5
Vertical Asymptotes - 400
• Use the table and graph to determine the vertical asymptote(s)
JJΣθPARδYΣθPARδY!! MαthMαth
Vertical Asymptote at x = -4
Y-intercepts - 100
• Find the y-intercept of the rational function
JJΣθPARδYΣθPARδY!! MαthMαth
(0, 5)
Y-intercepts - 200
• Find the y-intercept of the rational function
JJΣθPARδYΣθPARδY!! MαthMαth
(0, -6)
Y-intercepts - 300
• Find the y-intercept of the rational function
JJΣθPARδYΣθPARδY!! MαthMαth
(0, 0.375)
Y-intercepts - 400
• Find the y-intercept of the rational function
JJΣθPARδYΣθPARδY!! MαthMαth
(0, 1.5)
Horizontal Asymptotes - 100
• Determine the horizontal asymptote of the following rational function.
JJΣθPARδYΣθPARδY!! MαthMαth
y = 0
Horizontal Asymptotes - 200
• Determine the horizontal asymptote of the following rational function.
JJΣθPARδYΣθPARδY!! MαthMαth
y = 6
Horizontal Asymptotes - 300
• Determine the horizontal asymptote of the following rational function.
JJΣθPARδYΣθPARδY!! MαthMαth
y = 1
Horizontal Asymptotes - 400
• Determine the horizontal asymptote of the following rational function.
JJΣθPARδYΣθPARδY!! MαthMαth
No Horizontal Asymptote
Domain - 100
• What is the theoretical domain of the following rational function?
JJΣθPARδYΣθPARδY!! MαthMαth
All real numbers except x = -6
Domain - 200
• What is the theoretical domain of the following rational function?
JJΣθPARδYΣθPARδY!! MαthMαth
All real numbers except x = 2
• What is the theoretical domain of the following rational function?
Domain - 300
JJΣθPARδYΣθPARδY!! MαthMαth
All real numbers except x = 1
Domain - 400
• What is the practical domain of the rational equation
JJΣθPARδYΣθPARδY!! MαthMαth
Practical domain can only be determined within a specific scenario. Context must be present in order to determine practical domain. The theoretical domain of this function is all real numbers except d = 0.
Factoring a = 1 - 100
• Write the following in factored form
JJΣθPARδYΣθPARδY!! MαthMαth
(x + 4)(x + 5)
Factoring a = 1 - 200
• Write the following in factored form
JJΣθPARδYΣθPARδY!! MαthMαth
(x – 4)(x + 3)
Factoring a = 1 - 300
• Write the following in factored form
JJΣθPARδYΣθPARδY!! MαthMαth
(x – 8)(x – 2)
Factoring a = 1 - 400
• Write the following in factored form
JJΣθPARδYΣθPARδY!! MαthMαth
(x + 6)(x – 6)
Factoring a > 1 - 100
• Write the following in factored form
JJΣθPARδYΣθPARδY!! MαthMαth
(2x + 1)(x – 3)
Factoring a > 1 - 200
• Write the following in factored form
JJΣθPARδYΣθPARδY!! MαthMαth
(3x + 1)(x – 4)
Factoring a > 1 - 300
• Write the following in factored form
JJΣθPARδYΣθPARδY!! MαthMαth
(5p + 9)(p – 2)
Factoring a > 1 - 400
• Write the following in factored form
JJΣθPARδYΣθPARδY!! MαthMαth
k(7k + 9)